$$ \sqrt[4]{x^3 \sqrt{x} \sqrt{x}} = \sqrt[4]{x^3 \sqrt{x^2}} = \sqrt[4]{x^3 x} = \sqrt[4]{x^4} = |x| $$.
При $$ x = \sqrt[3]{4^4} $$, $$ |x| = |\sqrt[3]{4^4}| = \sqrt[3]{4^4} = \sqrt[3]{256} $$.
Ответ: $$ \sqrt[3]{256} $$.